The following equation represents a percent change on the value

Question

How can you describe this in words?

Responses

An increase of
is the same as multiplying by
An increase of 58 percent is the same as multiplying by

A decrease of
is the same as multiplying by
A decrease of 58 percent is the same as multiplying by

An increase of
is the same as multiplying by
An increase of 42 percent is the same as multiplying by

A decrease of
is the same as multiplying by
A decrease of 42 percent is the same as multiplying by

Answer 1

To describe the percent changes represented by the equations, we can summarize the ideas around both increases and decreases in percentage terms. Here’s a breakdown of your statements:

1. Increase:

   • An increase of X percent is the same as multiplying by (1 + X/100).
   • For instance:
     • An increase of 58 percent is the same as multiplying by (1 + 58/100), which simplifies to 1.58.
     • An increase of 42 percent is the same as multiplying by (1 + 42/100), which simplifies to 1.42.

2. Decrease:

   • A decrease of Y percent is the same as multiplying by (1 - Y/100).
   • For example:
     • A decrease of 58 percent is the same as multiplying by (1 - 58/100), which simplifies to 0.42.
     • A decrease of 42 percent is the same as multiplying by (1 - 42/100), which simplifies to 0.58.

In summary, an increase is represented by a multiplication factor greater than 1 (1 plus the percent expressed as a decimal), while a decrease is represented by a multiplication factor less than 1 (1 minus the percent expressed as a decimal).